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Ampere’s Law AP Physics C Mrs. Coyle Andre Ampere

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Remember: Biot-Savart Law: Field produced by current carrying wires –Distance a from long straight wire –Centre of a wire loop radius R –Centre of a Solenoid with N turns

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Remember: There are two ways to find the electric field around a charged object. Coulomb’s Law (Superposition) Gauss’s Law This is used for high symmetry cases.

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There are two ways to calculate magnetic field. Biot-Savart Law Ampere’s Law –Used for high symmetry cases.

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Ampere’s Law For small length elements ds on a closed path (not necessarily circular) I is enclosed current passing through any surface bounded by the closed path. Note: dot product Use where there is high symmetry ds I B

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Sign Convention for the Current in Ampere’s Law r The current I passing through a loop is positive if the direction of B from the right hand rule is the same as the direction of the integration (ds). r positive I I B ds I B negative I

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Field Outside a Long Straight Wire at a distance r from the center, r > R The current is uniformly distributed through the cross section of the wire

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Field Inside a Long Straight Wire at a distance r from the center, r< R Inside the wire, the current considered is inside the amperian circle Note the linear relationship of B with r

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Field Due to a Long Straight Wire The field is proportional to r inside the wire The field varies as 1/r outside the wire Both equations are equal at r = R

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Magnetic Field of a Toroid Find the field at a point at distance r from the center of the toroid The toroid has N turns of wire

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Magnetic Field of an Thin Infinite Sheet Rectangular amperian surface The w sides of the rectangle do not contribute to the field The two ℓ sides (parallel to the surface) contribute to the field J s =I/ l is the linear current density along the z direction The current is in the y direction

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Magnetic Field of a Solenoid The field lines in the interior are –approximately parallel to each other –uniformly distributed –close together The field is strong and almost uniform in the interior

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Magnetic Field of a Tightly Wound Solenoid The field distribution is similar to that of a bar magnet As the length of the solenoid increases –the interior field becomes more uniform –the exterior field becomes weaker

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Ideal Solenoid –The turns are closely spaced –The length is much greater than the radius of the turns

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Magnetic Field Inside a Long Solenoid -The total current through the rectangular path equals the current through each turn multiplied by the number of turns

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Note The magnetic field inside a long solenoid does not depend on the position inside the solenoid (if end effects are neglected).

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Magnetic Field –At a distance a from long straight wire –At the centre of a wire loop radius R –At the centre of a solenoid with N turns -In the interior of a toroid

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